The pro-\'etale cohomology of Drinfeld's upper half space

We determine the geometric pro-'etale cohomology of Drinfeld’s upper half space $\mathcal{X}$ over a p-adic field. The strategy is different from the one given by Colmez, Dospinescu and Niziol. It uses the approach developed in a former paper of the author describing global sections of equivariant vector bundles on $\mathcal{X}$.